Prior experience and patterning in a prisoner's dilemma game

Female college students first played a pseudo-prisoner's dilemma (PPD) game with the experimenter, who followed a fixed strategy. In the first experiment the experimenter's strategies for different groups of subjects were: (a) play tit-for-tat; (b) play randomly; (c) always cooperate; (d) always defect (‘cooperation’ and ‘defection’, defined as in an actual prisoner's dilemma game). Only the tit-for-tat group increased cooperation over trials; other groups decreased cooperation. After playing the PPD with the experimenter, subjects played an actual prisoner's dilemma (PD) game with each other. In the PD game, subjects began cooperating moderately but cooperation deteriorated regardless of what the experimenter's strategy had been in the earlier (PPD) game. In a second experiment, subjects again played a PPD game with the experimenter and then played a PD game with each other. Half played one trial at a time as in the first experiment while half played in patterns of four trials at a time. In the PD game, patterning of trials retarded the development of mutual defection regardless of previous experience. The cooperation-preserving effect of patterning of trials in this social task is compared with similar effects on individual tasks involving self-control and risk-aversion. © 1998 John Wiley & Sons, Ltd.     

Commitment and self-control in a prisoner's dilemma game

Humans often make seemingly irrational choices in situations of conflict between a particular smaller-sooner reinforcer and a more abstract, temporally extended, but larger reinforcer. In two experiments, the extent to which the availability of commitment responses-self-imposed restrictions on future choices-might improve self-control in such situations was investigated. Participants played a prisoner's dilemma game against a computer that played a tit-for-tat strategy-cooperating after a participant cooperated, defecting after a participant defected. Defecting produced a small-immediate reinforcer (consisting of points convertible to gift cards) whereas cooperating increased the amount of subsequent reinforcers, yielding a greater overall reinforcer rate. Participants were normally free to cooperate or defect on each trial. Additionally, they could choose to make a commitment response that forced their choice for the ensuing five trials. For some participants, the commitment response forced cooperation; for others, it forced defection. Most participants, with either commitment response available, chose to commit repeatedly despite a minor point loss for doing so. After extended exposure to these contingencies, the commit-to-cooperate group cooperated significantly more than a control group (with no commitment available). The commit-to-defect group cooperated significantly less than the control group. When both commitment alternatives were simultaneously available-one for cooperation and one for defection-cooperation commitment was strongly preferred. In Experiment 2, the commitment alternative was removed at the end of the session; gains in cooperation, relative to the control group, were not sustained in the absence of the self-imposed behavioral scaffold.     

Decision making in the prisoner's dilemma game: The effect of exit on cooperation and social welfare

The prisoner's dilemma game is a mixed‐motive game that offers two players the simultaneous choice between a cooperative and a defective alternative. An often neglected aspect of such a binary‐choice game, however, is that in many real‐life encounters, people can choose not only to cooperate or defect, but they also have a third option: to exit the social dilemma. Although in the literature a consensus has emerged that the addition of an exit opportunity benefits cooperation, there is only scant research into its effect on social welfare. In order to allow a direct comparison of cooperation rates and welfare levels across binary‐choice and trinary‐choice games, in this study, we used a design in which the same participants played similar games with and without an exit option (i.e., a within‐subjects design), and this in a range of structural variations. The findings of our study indicated that the aggregated outcome of both players is generally lower in games with an exit option than in games without an exit option. Moreover, our results showed that the efficiency of the exit option strongly depends on the specific outcome structure of the game (in terms of its endowment size, (a)symmetry, and level of noncorrespondence). In the discussion, it is argued that the implementation of an exit option as a strategy to increase social welfare should be critically assessed.     

Contingencies of reinforcement in a five-person prisoner's dilemma

As in studies of self-control, a tit-for-tat contingency in an iterated prisoner's dilemma game creates a conflict between maximization of local and global reinforcement. The present experiments examine this conflict in a multiplayer prisoner's dilemma game. Versus tit for tat, cooperation corresponds to self-control; defection, always immediately reinforced, corresponds to impulsiveness. Three experiments examined sensitivity of behavior to the global reinforcement contingency imposed by tit for tat. Undergraduates played a five-player prisoner's dilemma game against four dummy players programmed to play tit for tat or randomly. With tit for tat, a player's cooperation (or defection) increased dummy players' cooperation (or defection) on subsequent trials-reinforcing cooperation and punishing defection in the long run. Participants cooperated at a higher rate when the dummy players played tit for tat than when the dummy players played randomly. These results are consistent with findings in corresponding studies of self-control. Some participants, caught in a trap of mutual defection with the tit-for-tat playing dummy players, came to cooperate when the tit-for-tat contingency was reset ("forgiving" participants' previous defections) during a pause in the game. This increase was a result of the combined effects of a pause and reset; neither pausing nor resetting independently resulted in an increase in cooperation.     

Effects of initial choices in the prisoner's dilemma

In the two‐person prisoner's dilemma game (PDG), there is considerable evidence that the tit‐for‐tat (TFT) strategy is most effective in inducing the other person to cooperate. One of the important features of the TFT strategy is that it cooperates on the first trial. We varied the initial choices of a simulated other, and tested the effects of (a) initial choices (cooperation or defection), and (b) persistence of initial choices: unilateral cooperation (or defection) on the first trial, first two trials, or first four trials. Results showed that a cooperative strategy—one that starts with cooperative choices—induced greater cooperation than a strategy that started with defections. The results of this study clearly show that (a) a cooperative strategy—one that initiates unilateral cooperation at the outset and then adopts a TFT strategy—is very effective in inducing subsequent cooperation from the other party, (b) the effectiveness of a cooperative strategy varies directly with the cooperative orientation of the other party (a cooperative strategy is more effective against a cooperative than a competitive person), and (c) initial cooperation is more effective if it is repeated more than once. Copyright © 2002 John Wiley & Sons, Ltd.     

The role of autoshaping in cooperative two-player games between starlings

We report a study of the behavior of starlings in laboratory situations inspired by the “prisoner's dilemma.” Our purpose is to investigate some possible mechanisms for the maintenance of cooperation by reciprocity and to investigate the process of autoshaping at a trial-by-trial level. In Experiment 1, pairs of starlings housed in adjacent cages played a discrete-trial “game” in which food could be obtained only by “cooperation.” In this game, pecking at a response key eliminated the opportunity to obtain food but produced food for the partner. If neither bird pecked, neither had the opportunity to obtain food in that trial. Some level of cooperation persisted for several sessions whether the birds had been pretrained for a high or low probability of pecking at the key. The probability of a cooperative response was higher after trials in which the partner responded (and a reward was obtained) than after trials in which neither bird responded (and no reward was obtained), but the probability of a response was even higher after trials in which the same bird had responded, even though no reward was obtained by the actor in these trials. This behavior did not require visual presence of another player, because similar results were obtained in Experiment 2 (a replicate of Experiment 1 in which the members of the pair could not see each other) and in Experiment 3, a game in which each starling played with a computer responding with “tit for tat.” Using an omission schedule, in which food was given in all trials in which the bird did not peck, Experiment 4 showed that pecking could be maintained by autoshaping. In this experiment, overall probability of pecking decreased with experience, due to a drop in the tendency to peck in consecutive trials. The probability of pecking in trials following a reinforced trial did not decrease with experience. An implementation of the Rescorla–Wagner model for this situation was capable of reproducing molar, but not molecular, aspects of our results. The results violate the predictions of several game-theoretical models for the evolution of cooperation, including tit for tat, generous tit for tat, and the superior win-stay-lose-shift.     

No Place to Hide: When Shame Causes Proselfs to Cooperate

Shame is considered a social emotion with action tendencies that elicit socially beneficial behavior. Yet, unlike other social emotions, prior experimental studies do not indicate that incidental shame boosts prosocial behavior. Based on the affect as information theory, we hypothesize that incidental feelings of shame can increase cooperation, but only for self-interested individuals, and only in a context where shame is relevant with regards to its action tendency. To test this hypothesis, cooperation levels are compared between a simultaneous prisoner's dilemma (where “defect” may result from multiple motives) and a sequential prisoner's dilemma (where “second player defect” is the result of intentional greediness). As hypothesized, shame positively affected proselfs in a sequential prisoner's dilemma. Hence ashamed proselfs become inclined to cooperate when they believe they have no way to hide their greediness, and not necessarily because they want to make up for earlier wrong-doing.     

Exchanges of group-based favours: Ingroup bias in the prisoner's dilemma game with minimal groups in Japan and New Zealand

Japanese ( N  = 48) and New Zealander ( N  = 55) participants were first assigned to one of two minimal groups, and then played a prisoner's dilemma game twice with an ingroup member and twice with an outgroup member. In one of the two games they played with an ingroup (or outgroup) member, participants and their partner knew one another's group memberships (mutual-knowledge condition). In the unilateral-knowledge condition, only the participants knew the group membership of their partner, but the partner did not know the group membership of the participant. Ingroup bias in cooperation emerged only in the mutual-knowledge condition in both countries; in the unilateral-knowledge condition no ingroup bias emerged. Mediational analyses found that, in accord with predictions, cooperation in the mutual-knowledge condition is mediated by expectation of the partner's cooperation. Ingroup bias in the mutual-knowledge condition emerged only among those who identified with the ingroup. Results provide support for a group heuristics account of ingroup favouritism in the minimal group. According to this account, participants who face minimal groups activate an ecologically adaptive heuristic of unilaterally cooperating with members of the same group, expecting indirect repayment from others in the same group.     

Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r, to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation (K), our formulation of risk allows us to construct games that vary in risk (as indexed by r) while controlling for cooperativeness (as indexed by K). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.     

The Temporal Dynamics of Cooperation

Parties in real-world conflicts often attempt to punish each other's behavior. If this strategy fails to produce mutual cooperation, they may increase punishment magnitude. The present experiment investigated whether delay-reduction - potentially less harmful than magnitude increase - would generate mutual cooperation as interactions are repeated. Participants played a prisoner's dilemma game against a computer that played a tit-for-tat strategy, cooperating after a participant cooperated, defecting after a participant defected. For half of the participants, the delay between their choice and the computer's next choice was long relative to the delay between the computer's choice and their next choice. For the other half, long and short delays were reversed. The tit-for-tat contingency reinforces the other player's cooperation (by cooperating) and punishes the other player's defection (by defecting). Both rewards and punishers are discounted by delay. Consistent with delay discounting, participants cooperated more when the delay between their choice and the computer's cooperation (reward) or defection (punishment) was relatively short. These results suggest that, in real-world tit-for-tat conflicts, decreasing delay of reciprocation or retaliation may foster mutual cooperation as effectively as (or more effectively than) the more usual tactic of increasing magnitude of reciprocation or retaliation.     

A Description–Experience Gap in Social Interactions: Information about Interdependence and Its Effects on Cooperation

In social interactions, decision makers are often unaware of their interdependence with others, precluding the realization of shared long‐term benefits. In an experiment, pairs of participants played an Iterated Prisoner's Dilemma under various conditions involving differing levels of interdependence information. Each pair was assigned to one of four conditions: “No‐Info” players saw their own actions and outcomes, but were not told that they interacted with another person; “Min‐Info” players knew they interacted with another person but still without seeing the other's actions or outcomes; “Mid‐Info” players discovered the other's actions and outcomes as they were revealed over time; and “Max‐Info” players were also shown a complete payoff matrix mapping actions to outcomes from the outset and throughout the game. With higher levels of interdependence information, we found increased individual cooperation and mutual cooperation, driven by increased reciprocating cooperation (in response to a counterpart's cooperation). Furthermore, joint performance and satisfaction were higher for pairs with more information. We discuss how awareness of interdependence may encourage cooperative behavior in real‐world interactions. Copyright © 2013 John Wiley & Sons, Ltd.     

Self‐control in a Prisoner's Dilemma game: the role of trial spacing and an interfering task

Self‐control was studied in an iterated one‐player Prisoner's Dilemma game in which students' choices affected the payoff matrix on the next trial. The frequency of self‐control responses (choice of the smaller payoff now, but with the more generous payoff matrix more likely on the next trial) and defection responses (choice of the larger payoff now, but with the less generous payoff matrix more likely on the next trial) were measured. In Experiment 1, players achieved a criterion of five consecutive self‐control responses more quickly as a positive function of trial spacing, the presence between trials of a discriminative stimulus associated with the upcoming payoff matrix, and the probability that the self‐control or defection response would be reciprocated by the computer. Experiment 2 replicated the effect of trial spacing except when there was an interfering task during the interval, suggesting that trial spacing permits better appreciation of the contingencies. Copyright © 2006 John Wiley & Sons, Ltd.     

动机的概率意义——概率归并定理与Monty Hall问题的非贝叶斯解

本文探讨Monty Hall问题认知困惑的形成因素。通过对该问题数学结构的分析,导出一个与该问题的解密切相关的定理——概率归并定理;并依据该定理给出了Monty Hall问题的一种更直观的数学解。     

Cooperation and coordination across cultures and contexts: Individual,sociocultural, and contextual factors jointly influence decision making in the volunteer's dilemma game

What factors promote or hinder volunteering within organizations and groups? This paper simultaneously explores the impact of individual, contextual, and sociocultural variables on decision making in a special type of social dilemma: the volunteer's dilemma game (VDG). The VDG provides a controlled experimental method for studying volunteering behaviors in an anonymous interactive environment. We developed six variations of the VDG and administered them to economics students in five different cultures (N_total = 603). Among other things, these VDGs varied whether the potential benefits of volunteering were certain or uncertain. Although the overall level of volunteering did not vary substantially across most cultural groups, we found that culture interacted with the size and (un)certainty of the benefits associated with volunteering, to influence volunteering decisions. We also found that religiosity (but not religious affiliation per se) increases volunteering and that men are less likely to volunteer when the returns to doing so are certain. These results extend our knowledge of behaviors in the VDG, and their potential drivers, with clear implications for understanding how culture, individual characteristics, and context jointly influence prosocial behavior and coordination.     

When to (or not to) trust intelligent machines: Insights from an evolutionary game theory analysis of trust in repeated games

The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, users take the risk that such agents act in ways opposed to the users’ preferences or goals. It is often argued that people use trust as a cognitive shortcut to reduce the complexity of such interactions. Here we formalise this by using the methods of evolutionary game theory to study the viability of trust-based strategies in repeated games. These are reciprocal strategies that cooperate as long as the other player is observed to be cooperating. Unlike classic reciprocal strategies, once mutual cooperation has been observed for a threshold number of rounds they stop checking their co-player’s behaviour every round, and instead only check it with some probability. By doing so, they reduce the opportunity cost of verifying whether the action of their co-player was actually cooperative. We demonstrate that these trust-based strategies can outcompete strategies that are always conditional, such as Tit-for-Tat, when the opportunity cost is non-negligible. We argue that this cost is likely to be greater when the interaction is between people and intelligent agents, because of the reduced transparency of the agent. Consequently, we expect people to use trust-based strategies more frequently in interactions with intelligent agents. Our results provide new, important insights into the design of mechanisms for facilitating interactions between humans and intelligent agents, where trust is an essential factor.     

HOW SHOULD WE BEHAVE? A REVIEW OF REASONS AND PERSONS BY DEREK PARFIT

In this book Parfit attempts to develop a rational, non-religious ethics. Instead of asking, “What does God tell us to do?” he asks, “What does reason tell us to do?” Given a set of simple assumptions, he considers whether it is possible to be consistently selfish or consistently good. Analyses of personal dilemmas (problems of self-control) and moral dilemmas (problems of social cooperation) show that neither consistent selfishness nor consistent goodness is logically possible. Instead, a fine balance must be maintained between, on the one hand, our immediate versus long-term good and, on the other, our own good versus that of other people. Ultimately Parfit fails to develop a formula by which such a balance may be struck. Parfit''s analysis is consistent with behavioral analysis in its reductionistic view of the self and the parallel it draws between relations with other people and relations with oneself at other times. Parfit''s analysis is inconsistent with behaviorism in its view of the mind as internal, available to introspection, and able to cause behavior. His nonfunctional mentalism leads Parfit to inconsistencies and blocks the path to a consistent ethics. Teleological behaviorism''s view of the mind in terms of patterns of overt behavior is not hampered by these inconsistencies and may lead to a functional rather than purely rational ethics.     

道德与关系惩罚对初中生公共物品困境中合作行为的影响

本研究模拟公共物品两难困境范式,以初中生为被试,通过两个实验分别考察道德惩罚和关系惩罚对不同性别和社会价值取向个体合作行为的影响。结果发现:(1)两种惩罚条件下初中生的合作水平均显著高于无惩罚条件,但当惩罚撤除后只有关系惩罚条件下的效应还存在;(2)初中女生在两种惩罚条件下的合作水平均显著高于无惩罚条件,而男生只在关系惩罚条件下出现该情况;(3)亲社会取向与亲自我取向初中生在两种惩罚阶段均表现出更高的合作水平,但在惩罚撤除后,只有亲社会取向者保持了高合作水平。这些结果表明,关系惩罚的作用较为持久,且对男生的影响更为突出,不过两种惩罚在亲社会取向者身上均显现出延后效应。     

Mutual support in games: Some properties of Berge equilibria

The Berge equilibrium concept formalizes mutual support among players motivated by the altruistic social value orientation in games. We prove some basic results for Berge equilibria and their relations to Nash equilibria, and we provide a straightforward method for finding Berge equilibria in n-player games. We explore some specific examples, and we explain how the Berge equilibrium provides a compelling model of cooperation in social dilemmas. We show that the Berge equilibrium also explains coordination in some common interest games and is partially successful in explaining the payoff dominance phenomenon, and we comment that the theory of team reasoning provides alternative solutions to these problems.